For \(n =0,1,2,\ldots ,\)  let \({\mathcal {V}}_n({\mathbb {V}}^{d+1}, W_{{\beta },{\gamma },\mu })\)  denote the space of orthogonal polynomials
of degree \(n\)  in \((x,t)\)  variables with respect to the inner
product
\( {\langle }\cdot , \cdot {\rangle }_{{\beta },{\gamma },\mu }\)  on the paraboloid. Then \(\dim {\mathcal {V}}_n({\mathbb {V}}^{d+1}, W_{{\beta },{\gamma },\mu }) =\binom{n+d}{n}\) . An orthogonal basis of this space can be given in terms of the Jacobi polynomials
and the classical orthogonal polynomials on the unit ball [1]}. We will also need the norms of
these orthogonal polynomials.
